2.14 IsTransitiveRel

IsTransitiveRel( rel )

IsTransitiveRel returns true if the binary relation rel is transitive and false otherwise.

    gap> IsTransitiveRel( Relation( [ [ ], [ 1 ], [ 1, 2 ] ] ) );    
    true
    gap> IsTransitiveRel( Relation( [ [ 2, 3 ], [ 1, 3 ], [ 1, 2 ] ] ) );
    false 

A relation R subseteq {1, ..., n} x {1, ..., n} is transitive if (x, z) in R whenever (x, y) in R and (y, z) in R for some y in {1, ..., n}. (See also TransitiveClosure.)

   
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